Search

This draft article outlines a prediction challenge where the target is to forecast the number of fatalities in armed conflicts, in the form of the UCDP `best' estimates, aggregated to the VIEWS units of analysis. It presents the format of the contributions, the evaluation metric, and the procedures, and a brief summary of the contributions. The article serves a function analogous to a pre-analysis plan: a statement of the forecasting models made publicly available before the true future prediction window commences. More information on the challenge, and all data referred to in this document, can be found at https://viewsforecasting.org/research/prediction-challenge-2023., Comment: Forecasting competition, conflict forecasting, forecasting with uncertainty

High-rate remote entanglement between photon and matter-based qubits is essential for distributed quantum information processing. A key technique to increase the modest entangling rates of existing long-distance quantum networking approaches is multiplexing. Here, we demonstrate a temporally multiplexed ion-photon interface via rapid transport of a chain of nine calcium ions across 74 $\mathrm{\mu m}$ within 86 $\mathrm{\mu s}$. The non-classical nature of the multiplexed photons is verified by measuring the second-order correlation function with an average value of $g^{(2)}(0)$ = 0.060(13), indicating negligible crosstalk between the multiplexed modes. In addition, we characterize the motional degree-of-freedom of the ion crystal after transport and find that it is coherently excited to as much as $\bar{n}_\alpha\approx 110$ for the center-of-mass mode. Our proof-of-principle implementation paves the way for large-scale quantum networking with trapped ions, but highlights some challenges that must be overcome., Comment: 6 pages, 4 figures

Quantum rotors promise unique advantages for quantum sensing, quantum simulation, and quantum information processing. At present, a variety of systems ranging from nanoparticles to single molecules and trapped ions have demonstrated detection and control of rotational motion in and near the quantum regime. For future applications of quantum rotors, understanding their dynamics in the presence of ambient environments and decoherence will be critical. While other model quantum systems such as the harmonic oscillator have seen extensive experimental study of their decoherence dynamics, such experiments remain an open task for the rigid rotor. We present measurements of fundamental scaling relationships for decoherence of a quantum planar rotor realized with two trapped ions, and find excellent agreement with recent theoretical work., Comment: 9 pages + supplementary information, 3 + 4 figures

Trapped-ion applications, such as in quantum information, precision measurements, optical clocks, and mass spectrometry, rely on specialized high-performance ion traps. The latter applications typically employ traditional machining to customize macroscopic 3D Paul traps, while quantum information processing experiments usually rely on photo-lithographic techniques to miniaturize the traps and meet scalability requirements. Using photolithography, however, it is challenging to fabricate the complex three-dimensional electrode structures required for optimal confinement. Here we address these limitations by adopting a high-resolution 3D printing technology based on two-photon polymerization supporting fabrication of large arrays of high-performance miniaturized 3D traps. We show that 3D-printed ion traps combine the advantages of traditionally machined 3D traps with the miniaturization provided by photolithography by confining single calcium ions in a small 3D-printed ion trap with radial trap frequencies ranging from 2 MHz to 24 MHz. The tight confinement eases ion cooling requirements and allows us to demonstrate high-fidelity coherent operations on an optical qubit after only Doppler cooling. With 3D printing technology, the design freedom is drastically expanded without sacrificing scalability and precision so that ion trap geometries can be optimized for higher performance and better functionality.

Kaplan and Rajendran have recently demonstrated that non-linear and state-dependent terms can be consistently added to quantum field theory to yield causal non-linear time evolution in quantum mechanics. Causal non-linear theories have the unavoidable feature that their quantum effects are dramatically sensitive to the full physical spread of the quantum state of the system. As a result, such theories are not well tested by conventional atomic and nuclear spectroscopy. By using a well-controlled superposition of vibrational modes of a $^{40}$Ca$^+$ ion trapped in a harmonic potential, we set a stringent limit of $5.4\times 10^{-12}$ on the magnitude of the unitless scaling factor $\tilde{\epsilon}_{\gamma}$ for the predicted causal, non-linear perturbation.

Most near-term quantum information processing devices will not be capable of implementing quantum error correction and the associated logical quantum gate set. Instead, quantum circuits will be implemented directly using the physical native gate set of the device. These native gates often have a parameterization (e.g., rotation angles) which provide the ability to perform a continuous range of operations. Verification of the correct operation of these gates across the allowable range of parameters is important for gaining confidence in the reliability of these devices. In this work, we demonstrate a procedure for sample-efficient verification of continuously-parameterized quantum gates for small quantum processors of up to approximately 10 qubits. This procedure involves generating random sequences of randomly-parameterized layers of gates chosen from the native gate set of the device, and then stochastically compiling an approximate inverse to this sequence such that executing the full sequence on the device should leave the system near its initial state. We show that fidelity estimates made via this technique have a lower variance than fidelity estimates made via cross-entropy benchmarking. This provides an experimentally-relevant advantage in sample efficiency when estimating the fidelity loss to some desired precision. We describe the experimental realization of this technique using continuously-parameterized quantum gate sets on a trapped-ion quantum processor from Sandia QSCOUT and a superconducting quantum processor from IBM Q, and we demonstrate the sample efficiency advantage of this technique both numerically and experimentally., Comment: 29 pages, 12 figures. This manuscript supersedes arXiv:2101.04474

Simulation of the interaction of light with matter, including at the few-photon level, is important for understanding the optical and optoelectronic properties of materials, and for modeling next-generation non-linear spectroscopies that use entangled light. At the few-photon level the quantum properties of the electromagnetic field must be accounted for with a quantized treatment of the field, and then such simulations quickly become intractable, especially if the matter subsystem must be modeled with a large number of degrees of freedom, as can be required to accurately capture many-body effects and quantum noise sources. Motivated by this we develop a quantum simulation framework for simulating such light-matter interactions on platforms with controllable bosonic degrees of freedom, such as vibrational modes in the trapped ion platform. The key innovation in our work is a scheme for simulating interactions with a continuum field using only a few discrete bosonic modes, which is enabled by a Green's function (response function) formalism. We develop the simulation approach, sketch how the simulation can be performed using trapped ions, and then illustrate the method with numerical examples. Our work expands the reach of quantum simulation to important light-matter interaction models and illustrates the advantages of extracting dynamical quantities such as response functions from quantum simulations.

We investigate the feasibility of using electrons in a linear Paul trap as qubits in a future quantum computer. We discuss the necessary experimental steps to realize such a device through a concrete design proposal, including trapping, cooling, electronic detection, spin readout and single and multi-qubit gate operations. Numeric simulations indicate that two-qubit Bell-state fidelities of order 99.99% can be achieved assuming reasonable experimental parameters.

In this work, we derive analytic formulae that determine the effect of error mechanisms on one- and two-qubit gates in trapped ions and electrons. First, we analyze, and derive expressions for, the effect of driving field inhomogeneities on one-qubit gate fidelities. Second, we derive expressions for two-qubit gate errors, including static motional frequency shifts, trap anharmonicities, field inhomogeneities, heating, and motional dephasing. We show that, for small errors, each of our expressions for infidelity converges to its respective numerical simulation; this shows our formulae are sufficient for determining error budgets for high-fidelity gates, obviating numerical simulations in future projects. All of the derivations are general to any internal qubit state, and any mixed state of the ion crystal's motion that is diagonal in the Fock state basis. Our treatment of static motional frequency shifts, trap anharmonicities, heating, and motional dephasing apply to both laser-based and laser-free gates, while our treatment of field imhomogenieties applies to laser-free systems.

We demonstrate coupling between the motions of two independently trapped ions with a separation distance of 620 $\mu$m. The ion-ion interaction is enhanced via a room-temperature electrically floating metallic wire which connects two surface traps. Tuning the motion of both ions into resonance, we show flow of energy with a coupling rate of 11 Hz. Quantum-coherent coupling is hindered by strong surface electric-field noise in our device. Our ion wire-ion system demonstrates that room-temperature conductors can be used to mediate and tune interactions between independently trapped charges over distances beyond those achievable with free-space dipole-dipole coupling. This technology may be used to sympathetically cool or entangle remotely trapped charges and enable coupling between disparate physical systems.

Electrons and ions trapped with electromagnetic fields have long served as important high-precision metrological instruments, and more recently have also been proposed as a platform for quantum information processing. Here we point out that these systems can also be used as highly sensitive detectors of passing charged particles, due to the combination of their extreme charge-to-mass ratio and low-noise quantum readout and control. In particular, these systems can be used to detect energy depositions many orders of magnitude below typical ionization scales. As illustrations, we suggest some applications in particle physics. We outline a non-destructive time-of-flight measurement capable of sub-eV energy resolution for slowly moving, collimated particles. We also show that current devices can be used to provide competitive sensitivity to models where ambient dark matter particles carry small electric millicharges $\ll e$. Our calculations may also be useful in the characterization of noise in quantum computers coming from backgrounds of charged particles., Comment: 4 pages, 3 figures. v2: published version, now includes time-of-flight measurement application and more detailed comments on millicharged DM at q > 10^-5

We aim to illuminate how the microscopic properties of a metal surface map to its electric-field noise characteristics. In our system, prolonged heat treatments of a metal film can induce a rise in the magnitude of the electric-field noise generated by the surface of that film. We refer to this heat-induced rise in noise magnitude as a thermal transformation. The underlying physics of this thermal transformation process is explored through a series of heating, milling, and electron treatments performed on a single surface ion trap. Between these treatments, $^{40}$Ca$^+$ ions trapped 70~$\mu$m above the surface of the metal are used as detectors to monitor the electric-field noise at frequencies close to 1~MHz. An Auger spectrometer is used to track changes in the composition of the contaminated metal surface. With these tools we investigate contaminant deposition, chemical reactions, and atomic restructuring as possible drivers of thermal transformations.

Realistic quantum sensors face a trade-off between the number of sensors measured in parallel and the control and readout fidelity ($F$) across the ensemble. We investigate how the number of sensors and fidelity affect sensitivity to continuous and intermittent signals. For continuous signals, we find that increasing the number of sensors by $1/F^2$ for $F<1$ always recovers the sensitivity achieved when $F=1$. However, when the signal is intermittent, more sensors are needed to recover the sensitivity achievable with one perfect quantum sensor. We also demonstrate the importance of near-unity control fidelity and readout at the quantum projection noise limit by estimating the frequency components of a stochastic, intermittent signal with a single trapped ion sensor. Quantum sensing has historically focused on large ensembles of sensors operated far from the standard quantum limit. The results presented in this manuscript show that this is insufficient for quantum sensing of intermittent signals and re-emphasizes the importance of the unique scaling of quantum projection noise near an eigenstate., Comment: 5 pages, 4 figures

Trapped-ion quantum information processors store information in atomic ions maintained in position in free space via electric fields. Quantum logic is enacted via manipulation of the ions' internal and shared motional quantum states using optical and microwave signals. While trapped ions show great promise for quantum-enhanced computation, sensing, and communication, materials research is needed to design traps that allow for improved performance by means of integration of system components, including optics and electronics for ion-qubit control, while minimizing the near-ubiquitous electric-field noise produced by trap-electrode surfaces. In this review, we consider the materials requirements for such integrated systems, with a focus on problems that hinder current progress toward practical quantum computation. We give suggestions for how materials scientists and trapped-ion technologists can work together to develop materials-based integration and noise-mitigation strategies to enable the next generation of trapped-ion quantum computers., Comment: 19 pages, 7 figures, commments welcome, now with all the figures

We demonstrate trapping of electrons in a millimeter-sized quadrupole Paul trap driven at 1.6~GHz in a room-temperature ultra-high vacuum setup. Cold electrons are introduced into the trap by ionization of atomic calcium via Rydberg states and stay confined by microwave and static electric fields for several tens of milliseconds. A fraction of these electrons remain trapped longer and show no measurable loss for measurement times up to a second. Electronic excitation of the motion reveals secular frequencies which can be tuned over a range of several tens to hundreds of MHz. Operating a similar electron Paul trap in a cryogenic environment may provide a platform for all-electric quantum computing with trapped electron spin qubits., Comment: Version accepted by PRX

Analog quantum simulation is expected to be a significant application of near-term quantum devices. Verification of these devices without comparison to known simulation results will be an important task as the system size grows beyond the regime that can be simulated classically. We introduce a set of experimentally-motivated verification protocols for analog quantum simulators, discussing their sensitivity to a variety of error sources and their scalability to larger system sizes. We demonstrate these protocols experimentally using a two-qubit trapped-ion analog quantum simulator and numerically using models of up to five qubits.

Photon pairs produced in spontaneous parametric down-conversion are naturally entangled in their transverse spatial degrees of freedom including the orbital angular momentum. Pumping a non-linear crystal with a zero order Gaussian mode produces quantum correlated signal and idler photons with equal orbital angular momentum and opposite signs. Measurements performed on one of the photons prepares the state of the other remotely. We study the remote state preparation in this system from the perspective of its potential application to Quantum Thermodynamics., Comment: 6 pages, 7 figures

Optical modes possessing orbital angular momentum constitute a very useful platform for experimental studies on the quantum limits of Thermodynamics. Here, we present experimental results for entangled photon pairs subjected to thin turbulence simulated with spatial light modulators and interpret them in the context of the generalized Jarzysnki's fluctuation relation. By holographic measurement of the orbital angular momentum, we obtain the work distribution produced by the turbulence for single and double-sided turbulence channels. The use of the Klyshko's advanced wave picture allows us to interpret the experimental scheme as two-way processes in a fully quantum picture., Comment: 10 pages, 11 figures, two new appendices

We probe electric-field noise in a surface ion trap for ion-surface distances $d$ between 50 and 300 $\mu\mathrm{m}$ in the normal and planar directions. We find the noise distance dependence to scale as $d^{-2.6}$ in our trap and a frequency dependence which is consistent with $1/f$ noise. Simulations of the electric-field noise specific to our trap geometry provide evidence that we are not limited by technical noise sources. Our distance scaling data is consistent with a noise correlation length of about 100 $\mu\mathrm{m}$ at the trap surface, and we discuss how patch potentials of this size would be modified by the electrode geometry.

The study of non-equilibrium physics from the perspective of the quantum limits of thermodynamics and fluctuation relations can be experimentally addressed with linear optical systems. We discuss recent experimental investigations in this scenario and present new proposed schemes and the potential advances they could bring to the field.

We demonstrate the preparation and coherent control of the angular momentum state of a two-ion crystal. The ions are prepared with an average angular momentum of $7780\hbar$ freely rotating at 100~kHz in a circularly symmetric potential, allowing us to address rotational sidebands. By coherently exciting these motional sidebands, we create superpositions of states separated by up to four angular momentum quanta. Ramsey experiments show the expected dephasing of the superposition which is dependent on the number of quanta separating the states. These results demonstrate coherent control of a collective motional state described as a quantum rotor in trapped ions. Moreover, our work offers an expansion of the utility of trapped ions for quantum simulation, interferometry, and sensing.

The high degree of control available over individual atoms enables precision tests of fundamental physical concepts. In this Letter, we experimentally study how precision measurements can be improved by preparing entangled states immune to the dominant source of decoherence. Using \Ca ions, we explicitly demonstrate the advantage from entanglement on a precision test of local Lorentz invariance for the electron. Reaching the quantum projection noise limit set by quantum mechanics, we observe for bipartite entangled states the expected gain of a factor of two in the precision. Under specific conditions, multipartite entangled states may yield substantial further improvements. Our measurements improve the previous best limit for local Lorentz invariance of the electron using \Ca ions by factor of two to four to about $5\times10^{-19}$.

We probe electric-field noise near the metal surface of an ion trap chip in a previously unexplored high-temperature regime. We observe a non-trivial temperature dependence with the noise amplitude at 1-MHz frequency saturating around 500~K. Measurements of the noise spectrum reveal a $1/f^{\alpha\approx1}$-dependence and a small decrease in $\alpha$ between low and high temperatures. This behavior can be explained by considering noise from a distribution of thermally-activated two-level fluctuators with activation energies between 0.35~eV and 0.65~eV. Processes in this energy range may be relevant to understanding electric-field noise in ion traps; for example defect motion in the solid state and surface adsorbate binding energies. Studying these processes may aid in identifying the origin of excess electric-field noise in ion traps -- a major source of ion motional decoherence limiting the performance of surface traps as quantum devices., Comment: Version accepted by PRA, significantly expanded compared to v1

We describe the design, fabrication, and operation of a novel surface-electrode Paul trap that produces a radio-frequency-null along the axis perpendicular to the trap surface. This arrangement enables control of the vertical trapping potential and consequentially the ion-electrode distance via dc-electrodes only. We demonstrate confinement of single $^{40}$Ca$^+$ ions at heights between $50~\mu$m and $300~\mu$m above planar copper-coated aluminium electrodes. We investigate micromotion in the vertical direction and show cooling of both the planar and vertical motional modes into the ground state. This trap architecture provides a platform for precision electric-field noise detection, trapping of vertical ion strings without excess micromotion, and may have applications for scalable quantum computers with surface ion traps.

We describe a broadly applicable experimental proposal to search for the violation of local Lorentz invariance (LLI) with atomic systems. The new scheme uses dynamic decoupling and can be implemented in current atomic clocks experiments, both with single ions and arrays of neutral atoms. Moreover, the scheme can be performed on systems with no optical transitions, and therefore it is also applicable to highly charged ions which exhibit particularly high sensitivity to Lorentz invariance violation. We show the results of an experiment measuring the expected signal of this proposal using a two-ion crystal of $^{88}$Sr$^+$ ions. We also carry out a systematic study of the sensitivity of highly charged ions to LLI to identify the best candidates for the LLI tests., Comment: 8 pages, two figures in main text, one figure in the supplementary material

Many important chemical and biochemical processes in the condensed phase are notoriously difficult to simulate numerically. Often this difficulty arises from the complexity of simulating dynamics resulting from coupling to structured, mesoscopic baths, for which no separation of time scales exists and statistical treatments fail. A prime example of such a process is vibrationally assisted charge or energy transfer. A quantum simulator, capable of implementing a realistic model of the system of interest, could provide insight into these processes in regimes where numerical treatments fail. We take a first step towards modeling such transfer processes using an ion trap quantum simulator. By implementing a minimal model, we observe vibrationally assisted energy transport between the electronic states of a donor and an acceptor ion augmented by coupling the donor ion to its vibration. We tune our simulator into several parameter regimes and, in particular, investigate the transfer dynamics in the nonperturbative regime often found in biochemical situations.

Quantum statistics have a profound impact on the properties of systems composed of identical particles. In this Letter, we demonstrate that the quantum statistics of a pair of identical massive particles can be probed by a direct measurement of the exchange symmetry of their wave function even in conditions where the particles always remain spatially well separated and thus the exchange contribution to their interaction energy is negligible. We present two protocols revealing the bosonic or fermionic nature of a pair of particles and discuss possible implementations with a pair of trapped atoms or ions., Comment: 4+13 pages, v2 corresponds to the version published by PRL

Non-equilibrium thermodynamics and quantum information theory are interrelated research fields witnessing an increasing interest, both theoretical and experimental. This is manly due to the broadness of these theories, which found applications in many different fields of science, ranging from biology to the foundations of physics. Here, by employing the orbital angular momentum of light, we propose a new platform for studying non-equilibrium properties of high dimensional quantum systems. Specifically, we use Laguerre-Gaussian beams to emulate the energy eigenstates of a two-dimension quantum harmonic oscillator having angular momentum. These light beams are subjected to a process realized by a spatial light modulator and the corresponding work distribution is experimentally reconstructed employing a two-point measurement scheme. The Jarzynski fluctuation relation is then verified. We also demonstrate the operation of the system as a Maxwell's demon.

We propose a scheme to read out the spin of a single electron quantum bit in a surface Paul trap using oscillating magnetic field gradients. The readout sequence is composed of cooling, driving, amplification and detection of the electron's motion. We study the scheme in the presence of noise and trap anharmonicities at liquid helium temperatures. An analysis of the the four procedures shows short measurement times ($25~\mu$s) and high fidelities ($99.7\%$) are achievable with realistic experimental parameters. Our scheme performs the function of fluorescence detection in ion trapping schemes, highlighting the potential to built all-electric quantum computers based on trapped electron spin qubits.

The detailed characterization of non-trivial coherence properties of composite quantum systems of increasing size is an indispensable prerequisite for scalable quantum computation, as well as for understanding of nonequilibrium many-body physics. Here we show how autocorrelation functions in an interacting system of phonons as well as the quantum discord between distinct degrees of freedoms can be extracted from a small controllable part of the system. As a benchmark, we show this in chains of up to 42 trapped ions, by tracing a single phonon excitation through interferometric measurements of only a single ion in the chain. We observe the spreading and partial refocusing of the excitation in the chain, even on a background of thermal excitations. We further show how this local observable reflects the dynamical evolution of quantum discord between the electronic state and the vibrational degrees of freedom of the probe ion., Comment: 22 pages, 4 figures

We report on the design of a cryogenic setup for trapped ion quantum computing containing a segmented surface electrode trap. The heat shield of our cryostat is designed to attenuate alternating magnetic field noise, resulting in 120~dB reduction of 50~Hz noise along the magnetic field axis. We combine this efficient magnetic shielding with high optical access required for single ion addressing as well as for efficient state detection by placing two lenses each with numerical aperture 0.23 inside the inner heat shield. The cryostat design incorporates vibration isolation to avoid decoherence of optical qubits due to the motion of the cryostat. We measure vibrations of the cryostat of less than $\pm$20~nm over 2~s. In addition to the cryogenic apparatus, we describe the setup required for an operation with $^{\mathrm{40}}$Ca$^{\mathrm{+}}$ and $^{\mathrm{88}}$Sr$^{\mathrm{+}}$ ions. The instability of the laser manipulating the optical qubits in $^{\mathrm{40}}$Ca$^{\mathrm{+}}$ is characterized yielding a minimum of its Allan deviation of 2.4$\cdot$10$^{\mathrm{-15}}$ at 0.33~s. To evaluate the performance of the apparatus, we trapped $^{\mathrm{40}}$Ca$^{\mathrm{+}}$ ions, obtaining a heating rate of 2.14(16)~phonons/s and a Gaussian decay of the Ramsey contrast with a 1/e-time of 18.2(8)~ms.

Spontaneous symmetry breaking is a universal concept throughout science. For instance, the Landau-Ginzburg paradigm of translational symmetry breaking underlies the classification of nearly all quantum phases of matter and explains the emergence of crystals, insulators, and superconductors. Usually, the consequences of translational invariance are studied in large systems to suppress edge effects which cause undesired symmetry breaking. While this approach works for investigating global properties, studies of local observables and their correlations require access and control of the individual constituents. Periodic boundary conditions, on the other hand, could allow for translational symmetry in small systems where single particle control is achievable. Here, we crystallize up to fifteen 40Ca+ ions in a microscopic ring with inherent periodic boundary conditions. We show the ring's translational symmetry is preserved at millikelvin temperatures by delocalizing the Doppler laser cooled ions. This establishes an upper bound for undesired symmetry breaking at a level where quantum control becomes feasible. These findings pave the way towards studying quantum many-body physics with translational symmetry at the single particle level in a variety of disciplines from simulation of Hawking radiation to exploration of quantum phase transitions., Comment: 15 pages, 4 figures

Radio-frequency (rf) Paul traps operated with multifrequency rf trapping potentials provide the ability to independently confine charged particle species with widely different charge-to-mass ratios. In particular, these traps may find use in the field of antihydrogen recombination, allowing antiproton and positron clouds to be trapped and confined in the same volume without the use of large superconducting magnets. We explore the stability regions of two-frequency Paul traps and perform numerical simulations of small, multispecies charged-particle mixtures that indicate the promise of these traps for antihydrogen recombination., Comment: 11 pages, 10 figures

Galactic cosmic rays reach energies of at least a few Peta-electronvolts (1 PeV =$10^\mathbf{15}$ electron volts). This implies our Galaxy contains PeV accelerators (PeVatrons), but all proposed models of Galactic cosmic-ray accelerators encounter non-trivial difficulties at exactly these energies. Tens of Galactic accelerators capable of accelerating particle to tens of TeV (1 TeV =$10^\mathbf{12}$ electron volts) energies were inferred from recent gamma-ray observations. None of the currently known accelerators, however, not even the handful of shell-type supernova remnants commonly believed to supply most Galactic cosmic rays, have shown the characteristic tracers of PeV particles: power-law spectra of gamma rays extending without a cutoff or a spectral break to tens of TeV. Here we report deep gamma-ray observations with arcminute angular resolution of the Galactic Centre regions, which show the expected tracer of the presence of PeV particles within the central 10~parsec of the Galaxy. We argue that the supermassive black hole Sagittarius A* is linked to this PeVatron. Sagittarius A* went through active phases in the past, as demonstrated by X-ray outbursts and an outflow from the Galactic Centre. Although its current rate of particle acceleration is not sufficient to provide a substantial contribution to Galactic cosmic rays, Sagittarius A* could have plausibly been more active over the last $\gtrsim 10^{6-7}$ years, and therefore should be considered as a viable alternative to supernova remnants as a source of PeV Galactic cosmic rays., Comment: 29 pages, 7 figures, 3 tables, in press, for official published article see http://www.nature.com/nature/journal/v531/n7595/full/nature17147.html